Block #155,375

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 7:07:15 AM · Difficulty 9.8657 · 6,653,789 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

6056a6c12d0231dccd2bb1ff51a287ae7d0c584f221a9f9fd5f9608cbcc63b0f

View on Chainz ↗

Height

#155,375

Difficulty

9.865731

Transactions

Size

878 B

Version

Bits

09dda089

Nonce

273,610

Timestamp

9/8/2013, 7:07:15 AM

Confirmations

6,653,789

Mined by

⛏️ P2SHAPbo6zkCs895VA6W2mxvVzWGfmGzcXssbz

Merkle Root

0c41d827cd82e494357106fb8b91010bf139651b27c0f49b99fceeaeeb6260e5

Transactions (4)

Coinbase1fde5b881c39b1…6af780c342cf62

1 in → 1 out10.2900 XPM109 B

APbo6zkC…GzcXssbz

1b4c3af5313faa…485d53afee0c0d

1 in → 2 out8.2026 XPM226 B

AJek1RWt…rWAfH9s2 AGTJ3o7D…yYXqatFN

a4f8e3662221d8…d4e195b8c8d897

1 in → 2 out8.1398 XPM225 B

AHeaS5CE…uyrhMQ7S AcuM7XiJ…5uND8Jce

19c6218d6b0e14…d854be92e85791

1 in → 2 out7.9740 XPM227 B

AdvHwdt7…k4WbrHPF AXZvTo9z…YBDPsrv2

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.634 × 10⁹⁶(97-digit number)

16349687194399194768…88095773583225398879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.634 × 10⁹⁶(97-digit number)

16349687194399194768…88095773583225398879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.634 × 10⁹⁶(97-digit number)

16349687194399194768…88095773583225398881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.269 × 10⁹⁶(97-digit number)

32699374388798389537…76191547166450797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.269 × 10⁹⁶(97-digit number)

32699374388798389537…76191547166450797761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.539 × 10⁹⁶(97-digit number)

65398748777596779074…52383094332901595519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.539 × 10⁹⁶(97-digit number)

65398748777596779074…52383094332901595521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.307 × 10⁹⁷(98-digit number)

13079749755519355814…04766188665803191039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.307 × 10⁹⁷(98-digit number)

13079749755519355814…04766188665803191041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.615 × 10⁹⁷(98-digit number)

26159499511038711629…09532377331606382079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #155,375

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